In woodshop class, you must cut several pieces of wood to within 3/16 inch of the teacher's specifications. Let (s-x) represent the difference between the specification s and the measured length x of a cut piece.

(a)Write an absolute value inequality that describes the values of x that are within the specifications.

(b) The length of one piece of wood is specified to be s=5 1/8 inches. Describe the acceptable lengths for this piece.

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sqdancefan sqdancefan · Answer 1 · 2019-09-24T11:07:29+02:00

Answer:

(a) |s - x| ≤ 3/16

(b) 4 15/16 ≤ x ≤ 5 5/16

Step-by-step explanation:

(a) The absolute value of the difference from spec must be no greater than than the allowed tolerance:

|s - x| ≤ 3/16

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(b) Put 5 1/8 for s in the above equation and solve.

|5 1/8 - x| ≤ 3/16

-3/16 ≤ 5 1/8 -x ≤ 3/16

3/16 ≥ x -5 1/8 ≥ -3/16 . . . . multiply by -1 to get positive x

5 5/16 ≥ x ≥ 4 15/16 . . . . . . add 5 1/8

Pieces may be between 4 15/16 and 5 5/16 inches in length.